Legendre is best known as the author of Éléments de géométrie, which was published in 1794 and was the leading elementary text on the topic for around 100 years. This text greatly rearranged and simplified many of the propositions from Euclid's Elements to create a more effective textbook.
His name is one of the 72 names inscribed on the Eiffel Tower.
"Legendre’s most famous book was the classic Eléments de Géométrie (1794), the leading elementary
geometry textbook for 100 years, widely used as a substitute for Euclid’s Elements. It was considered a
pedagogical improvement because Legendre rearranged and simplified the propositions. The text,
greatly admired on the continent, became the prototype of elementary geometry textbooks in the United
States when John Farrar of Harvard University translated it into English in 1891. The celebrated man of
letters, Thomas Carlyle, who as a young man taught mathematics, made another English translation of
Legendre’s geometry, which ran through 33 American editions. Later editions of Legendre’s geometry
contained elements of trigonometry as well as his proofs of the irrationality of π and π2. In the 1803
edition Legendre included an appendix dealing with his attempts to prove the parallel postulate, a task
with preoccupied him for 30 years. Even when Bolyai published his work creating non-Euclidean
geometry, Legendre stubbornly clung to the belief that Euclidean geometry was the only certainty. He
published his last article on the parallel postulate the year of his death."
-excerpt from: http://www.robertnowlan.com/pdfs/Legendre,%20Adrien-Marie.pdf
"the sum of angles of a triangle is 180 degrees" -from our notes
- "Legendre’s most famous book was the classic Eléments de Géométrie (1794), the leading elementary
geometry textbook for 100 years, widely used as a substitute for Euclid’s Elements. It was considered apedagogical improvement because Legendre rearranged and simplified the propositions. The text,
greatly admired on the continent, became the prototype of elementary geometry textbooks in the United
States when John Farrar of Harvard University translated it into English in 1891. The celebrated man of
letters, Thomas Carlyle, who as a young man taught mathematics, made another English translation of
Legendre’s geometry, which ran through 33 American editions. Later editions of Legendre’s geometry
contained elements of trigonometry as well as his proofs of the irrationality of π and π2. In the 1803
edition Legendre included an appendix dealing with his attempts to prove the parallel postulate, a task
with preoccupied him for 30 years. Even when Bolyai published his work creating non-Euclidean
geometry, Legendre stubbornly clung to the belief that Euclidean geometry was the only certainty. He
published his last article on the parallel postulate the year of his death."
-excerpt from: http://www.robertnowlan.com/pdfs/Legendre,%20Adrien-Marie.pdf